The story of modern British sculpture could be said to resemble the famous episode in the Divine Comedy when, passing through purgatory, Dante thinks he recognises the Umbrian miniaturist Oderisi – once the "glory" of Gubbio. The painter laments that his fame has been eclipsed by that of his hated rival, Franco Bolognese – whose brighter colours have "all the honour now; my light obscured" – and confesses he is being punished for the pride that made him so desperate to be pre-eminent.

Oderisi mentions two other artists embroiled in reputational war:

Cimabue thoughtTo lord it over painting's field; and nowThe cry is Giotto's, and his name eclipsed.

Dante is moved to consider how the poet Guido Cavalcanti has usurped Guido Guinicelli, and to wonder whether another poet (ie himself) will "drive either from their nest". This passage arguably enshrined the concept of intergenerational jockeying between practitioners in the history of art, as Dante's rather half-hearted critique of the fame game – it is Oderisi, not the poet, who says "O powers of man! How vain your glory" – gave a tacit green light to artistic self-assertion and the idea of aesthetic obsolescence.

British sculpture, then, is often seen as a Dantean battleground, with new generations eclipsing their forebears and consigning them to creative limbo. Thus Henry "carver" Moore was driven from the nest by his former assistant Anthony "welder" Caro, producer of brightly painted metal sculptures, and Caro in turn was overturned by former students Richard "walker" Long and Barry "arranger" Flanagan. Then, in the 1980s, it was the turn of Tony "scavenger" Cragg, whose first assemblages were a colourful post-industrial riposte to Long's ascetic pastoralism. For a decade, Cragg was the sculptor on everyone's lips and every curator's wishlist. At the end of the 80s, he scored a notable hat-trick with a solo show at the Hayward, victory in the Turner prize and selection to represent Britain at the Venice Biennale.

So just where does Cragg stand now, after successive sculptural whirlwinds set in motion by Hirst and assorted YBAs, and the swift rise of his formerly overshadowed contemporaries, Antony Gormley and Anish Kapoor? For most British gallery-goers under the age of 40, it's a case of "Tony who?" This new Edinburgh exhibition is an attempt to remind us what all the fuss was about, and to suggest that, after his 80s heyday, Cragg has had a second and third wind. Most, though not all, of the work is from the last 20 years.

Scotland is the perfect place for a Cragg show, as his most celebrated work is Britain Seen from the North (1981), a bright, 22ft mosaic map of the mainland put together from scavenged plastic objects, some broken, some intact. The piece is always pinned to the wall sideways, with Wales next to the floor as in the medieval Gough Map, and is "seen" by a mosaic figure (a life-size self-portrait) standing a few feet away from the northern tip of Scotland. It recalls the terra incognita of the middle ages – an uncharted no man's land populated by monsters and marvels. In 1981, Britain was in turmoil, with unemployment rising to unprecedented figures; the year opened with the miners' strike and the summer was scarred by the Toxteth riots. When this work was shown at the Whitechapel Gallery that year (along with similar reliefs of a Union flag, the crown jewels and a riot policeman), it was instantly embraced as the perfect cipher for the nation's troubled soul. It was bought by the Tate in 1982, and has been frequently displayed.

Cragg was born in Liverpool in 1949, and initially planned to follow a similar career to his peripatetic father, who worked as an electrical engineer in the aircraft industry and helped develop the Concorde. In 1966, at 17, Cragg began work as a lab technician at the National Rubber Producers' Research Association in Welwyn Garden City. During the long, slack periods spent "watching things tick and boil", he started making drawings to help him visualise the biochemical processes; in 1968 he left to pursue this interest, studying for three years at Wimbledon School of Art and five more at the Royal College in London. It was the time of conceptualism and Arte Povera, with their cults of unconventional media. At Wimbledon Cragg was taught by Roger Ackling, who worked with found and discarded pieces of wood, using the sun's rays and a magnifying glass to burn abstract lines and images into them. Ackling introduced the budding sculptor to his friend and fellow land artist, Richard Long.

Cragg's early work was an urban critique of the older men's pastoral fixation. You could now fill a thousand Tate Moderns with post-industrial pastiches of Long's minimalist stone lines and circles, but Cragg was one of the first to bite the hand that had fed him. He has denied any ironic intent, but in some photo pieces from the early 1970s (taken by Ackling in the Isle of Wight) he arranged lines and circles of white stones across his elegantly besuited body, and in the mid-70s made circular floor pieces from broken plates and variously coloured brick and cement rubble. Cragg found inspiration and materials during his part-time work on building sites, and on foraging expeditions around London. In 1978 he produced a pair of impeccable Long-style panoramic landscape photographs – except that they were of quarries and titled Cement Works. It was also then that he started to make figurative floor and wall pieces from found objects made of brightly coloured plastic.

After marrying a German trainee teacher in 1977, Cragg moved to her hometown of Wuppertal in the Ruhr, West Germany's industrial heartland, because her teaching exams required her to spend a year there. He soon got a teaching post in Düsseldorf – fiefdom of charismatic sculptor and shaman Joseph Beuys, that great modern poet of industrial materials and processes – and the move to Germany became permanent. But throughout the 80s, Cragg was still very much regarded and marketed as a British artist, grouped together with other quasi-figurative sculptors such as Richard Deacon, Bill Woodrow, Richard Wentworth, Shirazeh Houshiary, Alison Wilding, Gormley and Kapoor, most of whom were represented by Nicholas Logsdail's Lisson Gallery. But Cragg clearly seemed to revel in his offshore, outsider status – as is only too apparent in Britain Seen from the North. In another wall relief from this period, Self-Portrait with Sack (1980), a plastic mosaic figure looks down at a real duffel bag, perhaps imagining life as a wanderer or vagrant.

Cragg's early success, however, owed more to his work's sympathy with international painting trends than with British sculptural developments. In the late 70s, a movement known variously as neo-expressionism or New Image Painting revived gestural figurative styles, with an institutional seal of approval given by the Royal Academy's A New Spirit in Painting exhibition in 1981. These works were a reaction against the more austere, esoteric and anti-commercial extremes of conceptual art. Vast canvases, thick impastos, raw handling and melodramatic, performance art-style imagery were the order of the day, and pieces sold for vast sums. Leading lights such as Anselm Kiefer and Julian Schnabel encrusted the surfaces of their painting with, respectively, straw and broken plates. Cragg's mosaics were hailed as a sculptural equivalent.

However topical his work's content, Cragg adopted, in interviews and written texts, a quasi-scientific aura of objectivity that sidestepped political implications. At any rate, he usually left it up to the viewer to decide. In 1981, he wrote an artist's statement using conceptual art's robotically laconic, passive-aggressive house style:

Simple processes. With materials no one else wants. Ideas that interest me. Images that interest me. Made where people let me make them. The rooms, the walls, the floors. The physical framework. Emotional responses. Intellectual responses. Elegant works. Humorous works. Beautiful works. Decorative works. Ugly works. Works in which I learned from the materials. Works like pictures. Meanings I intended. Meanings that surprised me. Personal references. Cultural references. No references.

A central mission was to erode the distinction between the man-made and natural worlds: "A bird's nest is obviously in the realm of nature, but a house is rarely considered as such." Plastic interested him, both because it was stridently artificial and also because it had less of a "balloon of information around it" than wood, bronze or stone. Cragg saw the ideal artist as an alchemist whose job it was to imbue such modern materials with poetic resonance – to give plastic some interesting cultural baggage.

Then, from the mid-80s, the outsider performed a seeming volte-face, taking up more permanent and expensive materials in the form of wood, plaster, stone, fibreglass, Kevlar, stainless steel, and above all, bronze. Cragg was well aware of the heavy associations of the last, not least due to the multiple-cast monuments that littered the later career of a certain arch-patriarch: "I knew that I had to make a sculpture in bronze but it took almost a year to pluck up the courage; the Henry Moore legacy loomed over us and I just kept thinking, 'I don't want to do that.'" Even so, he did become something of a Moore-style elder statesman himself, setting up his own foundation and dispatching from a large studio durable and mostly bland monoliths for plazas, parks and atria around the world. As soon as he did so, he all but disappeared from the map of cutting-edge British art.

Cragg accepted a CBE in 2002, and in 2009 was appointed director of the Düsseldorf Kunstakademie. He also opened a 30-acre sculpture park in a forest in Wuppertal, run by the Cragg Foundation, to showcase his own bronzes and mount sculpture exhibitions. Some of the bronzes in the long-running Early Forms series are uncannily Moore-like, resembling pestles, bottles and laboratory receptacles that have melted into irregular but streamlined biomorphic shapes. Placed directly on the floor, they seem to want to drag Moore's reclining figures into the age of genetic engineering. They are not "early" in the sense of primordial, but forms captured in the first stages of an artificial life cycle.

Cragg has generally preferred a stark clarity of form and content in his work. The big danger in this approach is slickness and glibness: the crown jewels composed from plastic detritus and the chemistry-kit Moore mockups are almost one-liners. Cragg is always at his best when you feel an idea, a form or a material has just run away with him. Works in which, as he put it, "I learned from the materials", and where he discovered "meanings that surprised me".

The best recent sculptures are vertical rather than horizontal in orientation and evoke standing figures, columns and towers, spinning helter-skelter on their axes and wobbling like a viscous liquid (the bronze is unbelievably smooth and polished). Here you sense an instinctive rather than a rehearsed instability, and get a giddy rush of exciting associations. Points of View (2004), made using computer-aided design, is a hydra-headed stainless steel monster with three main "trunks", each resembling a precariously piled stack of spinning plates – though what are actually stacked are schematically mapped outlines of human profiles: noses, mouths, chins, eye-sockets. Cragg must have been thinking of Max Ernst's dadaist collage The Hat Makes the Man (1920) – in which images of bowler hats are composed into phallic towers – or Renato Bertelli's futurist bust of Mussolini in the Imperial War Museum, in which the dictator's profile is spun through 360 degrees to suggest his omnivoyance. Some of Cragg's related drawings, also included in this exhibition, recall Characters and Caricaturas, Hogarth's engraved pile-up of profiles.

The end result – a cacophonous conversation piece, perhaps dramatising information overload – is sui generis: a newly discovered life-form.